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How powerful are folding/unfolding transformations?

Part of: JFP Research Articles

Published online by Cambridge University Press:  07 November 2008

Hong Zhu
Hong Zhu
Affiliation:
Institute of Computer Software, Nanjing University, Nanjing, PR China, Department of Computing, The Open University, UK
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Abstract

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This paper discusses the transformation power of Burstall and Darlington's folding/unfolding system, i.e. what kind of programs can be derived from a given one. A necessary condition of derivability is proved. The notion of inherent complexity of recursive functions in introduced. A bound on efficiency gain by folding/unfolding transformations is obtained for all reasonable computation models. The well-known partial correctness and incompleteness of the system are corollaries of the result. Examples of underivability are given, e.g. binary searching cannot be derived from linear searching, merge sorting cannot be derived from insert sorting.

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Type
Articles
Information
Journal of Functional Programming , Volume 4 , Issue 1 , January 1994 , pp. 89 - 112
Copyright
Copyright © Cambridge University Press 1994

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